Find Three Ordered Pair Solutions 3x-7y=19

$3 x - 7 y = 19$

Step 1

Solve the equation for $y$ .

Subtract $3 x$ from both sides of the equation.

$- 7 y = 19 - 3 x$

Divide each term in $- 7 y = 19 - 3 x$ by $- 7$ and simplify.

Divide each term in $- 7 y = 19 - 3 x$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{19}{- 7} + \frac{- 3 x}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{19}{- 7} + \frac{- 3 x}{- 7}$

Divide $y$ by $1$ .

$y = \frac{19}{- 7} + \frac{- 3 x}{- 7}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{19}{7} + \frac{- 3 x}{- 7}$

Dividing two negative values results in a positive value.

$y = - \frac{19}{7} + \frac{3 x}{7}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = - \frac{19}{7} + \frac{3 (0)}{7}$

Simplify $- \frac{19}{7} + \frac{3 (0)}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{- 19 + 3 (0)}{7}$

Simplify the expression.

Multiply $3$ by $0$ .

$y = \frac{- 19 + 0}{7}$

Add $- 19$ and $0$ .

$y = \frac{- 19}{7}$

Move the negative in front of the fraction.

$y = - \frac{19}{7}$

Use the $x$ and $y$ values to form the ordered pair.

$(0, - \frac{19}{7})$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = - \frac{19}{7} + \frac{3 (1)}{7}$

Simplify $- \frac{19}{7} + \frac{3 (1)}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{- 19 + 3 (1)}{7}$

Simplify the expression.

Multiply $3$ by $1$ .

$y = \frac{- 19 + 3}{7}$

Add $- 19$ and $3$ .

$y = \frac{- 16}{7}$

Move the negative in front of the fraction.

$y = - \frac{16}{7}$

Use the $x$ and $y$ values to form the ordered pair.

$(1, - \frac{16}{7})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = - \frac{19}{7} + \frac{3 (2)}{7}$

Simplify $- \frac{19}{7} + \frac{3 (2)}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{- 19 + 3 (2)}{7}$

Simplify the expression.

Multiply $3$ by $2$ .

$y = \frac{- 19 + 6}{7}$

Add $- 19$ and $6$ .

$y = \frac{- 13}{7}$

Move the negative in front of the fraction.

$y = - \frac{13}{7}$

Use the $x$ and $y$ values to form the ordered pair.

$(2, - \frac{13}{7})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{19}{7}), (1, - \frac{16}{7}), (2, - \frac{13}{7})$

Step 7

Find Three Ordered Pair Solutions 3x-7y=19

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